Pith Number

pith:QQ2MT25W

pith:2021:QQ2MT25WDGY5L35QO4FVYIMYZK

not attested not anchored not stored refs pending

Dilation of stochastic matrices by coarse graining

Heinz-J\"urgen Schmidt

arxiv:2106.03513 v1 · 2021-06-07 · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QQ2MT25WDGY5L35QO4FVYIMYZK}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

The Born Representation Theorem and the Unistochastic Theorem

Receipt and verification

First computed	2026-07-05T02:46:50.244752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8434c9ebb619b1d5efb0770b5c2198caa1185e60775df32f6db7c3e7b239aa0f

Aliases

arxiv: 2106.03513 · arxiv_version: 2106.03513v1 · doi: 10.48550/arxiv.2106.03513 · pith_short_12: QQ2MT25WDGY5 · pith_short_16: QQ2MT25WDGY5L35Q · pith_short_8: QQ2MT25W

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QQ2MT25WDGY5L35QO4FVYIMYZK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8434c9ebb619b1d5efb0770b5c2198caa1185e60775df32f6db7c3e7b239aa0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "690b7c3a46e8e249a6fdfae2cdf6b5a2d19d473d827abd3da57343bb481c6a97",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2021-06-07T11:05:48Z",
    "title_canon_sha256": "ad62c0e3b1a26848f78154d201084b65e35ee8de2779ceb7fd005ad01b5bcc70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.03513",
    "kind": "arxiv",
    "version": 1
  }
}